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Algorithmic Aspects of Symbolic Switch Network Analysis
 IEEE Trans. CAD/IC
, 1987
"... A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean eq ..."
Abstract

Cited by 16 (5 self)
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A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean equations. For the class of networks that arise when analyzing digital metaloxide semiconductor (MOS) circuits, a simple pivot selection rule guarantees that most s switch networks encountered in practice can be solved with O(s) operations. When represented by a directed acyclic graph, the set of Boolean formulas generated by the analysis has total size bounded by the number of operations required by the Gaussian elimination. This paper presents the mathematical basis for systems of Boolean equations, their solution by Gaussian elimination, and data structures and algorithms for representing and manipulating Boolean formulas.
A Comparison of Computational Complexities of HFEM and ABC Based Finite Element Methods
"... The solution of a hybrid finite element method (HFEM) problem is considered. It is shown that a suitable ordering of the FEM mesh results in a canonical HFEM matrix system. This linear system can be solved in O(N 1:5 ) cost when sparse direct methods are used. This cost is comparable to FEM method ..."
Abstract
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The solution of a hybrid finite element method (HFEM) problem is considered. It is shown that a suitable ordering of the FEM mesh results in a canonical HFEM matrix system. This linear system can be solved in O(N 1:5 ) cost when sparse direct methods are used. This cost is comparable to FEM methods using approximate boundary conditions and a similar sparse solution method. I. Introduction Surface integral equations have been used in the past as boundary conditions for electromagnetic problems. Their use as a boundary condition was first reported in the work of McDonald and Wexler [1]. When surface integral equations are used as boundary conditions for FEM, the method is called the hybrid finite element method (HFEM). Researchers have used this method to solve openregion electromagnetic scattering problems [2, 3]. Sparse linear systems associated with an FEM formulation typically have nonzeros clustered within a small band along the diagonal. Sparse direct solvers can exploit this p...